CONNECTIVITY OF SOFT RANDOM GEOMETRIC GRAPHS
成果类型：
Article
署名作者：
Penrose, Mathew D.
署名单位：
University of Bath
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/15-AAP1110
发表日期：
2016
页码：
986-1028
关键词：
摘要：
Consider a graph on n uniform random points in the unit square, each pair being connected by an edge with probability p if the inter-point distance is at most r. We show that as n -> infinity the probability of full connectivity is governed by that of having no isolated vertices, itself governed by a Poisson approximation for the number of isolated vertices, uniformly over all choices of p, r. We determine the asymptotic probability of connectivity for all (p(n), r(n)) subject to r(n) = o(n(-epsilon)), some epsilon > 0. We generalize the first result to higher dimensions and to a larger class of connection probability functions.